Fr T.J. Linane, From Abel to Zundolovich, Vol. 2: Biographies of Priests on the Australian Scene up to 1900, 1980, p 7:

Byrne, Moses Hilarion, O.Carm., Irish
First Carmelite Group in Australia
His Parents were Matthias Byrne and Maria Price; and he was born on 20.9.1853 in Naas, County Kildare. According to Fr. John Ryan CSSp Blackrock College, Dublin. Hilarion was at Blackrock as a youth of 15, in the years 1868-9. After joining the Carmelite Fathers he studied in Ireland and Rome, being ordained in Rome 1.11.1880. In March 1881 he was among the first Carmelites to sail for Australia: Frs. Butler, Carr, Leybourne, Stone being the others. On arrival in Adelaide on April 18 they were assigned to the parish of Gawler, where they had charge of four churches and several scattered stations. Moses (religious name) Hilarion is credited with completing the church of St. Malachy's at Mallalla in 1882. Shortly after this he appears to have joined the first group of Carmelites to come to Port Melbourne (April 1882). He gave service to the Gawler and Port Melbourne parishes until March 1889, returning to Whitefriars, Dublin. Very little is recorded of his priestly activity in Australia and Ireland; but we can assign to him the same credit that can be assigned to all Carmelites who have worked in Australia: a splendid contribution to the build-up of a Marian devotion through the Brown Scapular enrolment. Moses Hilarion died suddenly in Dublin on 14.10.1896, at the age of 53. Burial took place at Glasnevin.
(Footprints, Vol. 1, No. 11)
Ref.: MDHC File, Torquay, per Liam Byrne Dublin Library & Fr. Gordon Carter, O'Carm.